Centre's radar showed you had a Ground Speed of 239kts at what altitude? Are we talking during level flight in cruise, at the start of your descent so 9,500ft or somewhere further down the descent?
If you're talking at the beginning then assuming you were maintaining VNO of 167kt IAS in the descent then you'd have about 200kts of TAS and therefore with a tailwind of 30kts you'd be at ~230kts GS which would reduce as you descend assuming tail wind stays the same and you maintain IAS of 167kts.
Things change if you're talking further down the descent though, say that reading from Centre was down around 3000feet you're more likely at 176kts TAS, if the 30kts tailwind has stayed the same all the way then you should be doing ~206kts GS, if you were still doing 239kts GS then you'd have had to be doing over 200kts IAS.
BUT this would be a relatively unusual situation having a tailwind of 30kts staying the same all the way down instead of more likely decreasing. In the more likely situation of the tailwind decreasing then it paints a grim picture of what your IAS was.
What you're saying though doesn't make sense overall, you're talking about trimming for VNO in the descent but then that the Aircraft is going to increase in GS simply by pointing the nose down, you also don't mention anything about what you're doing with the throttle so this all doesn't make much sense.